Harmonic Shape Images: A Representation for 3D Free-Form Surfaces Based on Energy Minimization

A new representation called Harmonic Shape Images for 3D free-form surfaces is proposed in this paper. This representation is based on the well-studied theory of Harmonic Maps which studies the mapping between different metric manifolds from the energyminimization point of view. The basic idea of Harmonic Shape Images is to map a 3D surface patch with disc topology to a 2D domain and encode the shape information of the surface patch into the 2D image. Due to the application of harmonic maps in generating Harmonic Shape Images, Harmonic Shape Images have the following advantages: they preserve both the shape and the continuity of the underlying surfaces, they are robust to occlusion and they are independent of surface sampling strategy. The proposed representation is applied to solve the surface-registration problem. Experiments have been conducted on real data and results are presented in the paper.

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